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If cos theta = 1/2 (x 1/x ) then prove that cos2 theta = 1/2 ( x^2 1/x^2)?
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If cos theta = 1/2 (x 1/x ) then prove that cos2 theta = 1/2 ( x^2 ...
Proof:

Given: cosθ = 1/2 (x + 1/x)

To prove: cos^2θ = 1/2 (x^2 + 1/x^2)

Proof:

We know that cos^2θ = (cosθ)^2

Using the given equation, we can substitute the value of cosθ:

cos^2θ = (1/2 (x + 1/x))^2

Simplifying the expression:

cos^2θ = (1/2)^2 (x + 1/x)^2

cos^2θ = 1/4 (x^2 + 2 + 1/x^2)

cos^2θ = 1/4 (x^2 + 1/x^2 + 2)

Since we need to prove that cos^2θ = 1/2 (x^2 + 1/x^2), we can see that the expression obtained above is not equal to the desired expression.

Therefore, the given statement is incorrect.

Hence, we cannot prove that cos^2θ = 1/2 (x^2 + 1/x^2) using the given equation.
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If cos theta = 1/2 (x 1/x ) then prove that cos2 theta = 1/2 ( x^2 1/x^2)?
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